Lets cut out plane !

Think about one line. It divides in 2 parts. Now about 2 lines. They divide a plane in 4 parts. 3 lines? 7 parts. 4? 11 parts. This might give an idea that number of parts must be $ax^2+bx+c$ where x is number of lines! ( $x^2$ because differece forms AP). By plugging in x=1,2,3, we will get $a=\frac{1}{2},\ b=\frac{1}{2},\ c=1$

Hence max number of parts in which n lines may divide a plane are $\frac{n^{2}+n}{2}+1$ .

By substituting $n=25$ , we will get number of parts to be $\boxed{326}$

There can be a simple formula for this $2n+ \frac{(n-2)(n-1)}{2}$ where $n$ is the no of lines substituting n with $25$ we get $50 + \frac{23 \times 24}{2}$ $= 50 + 276$ $=326$